I had similar problem with long SMS, roughly greater than 64 char, with Arduino UNO R3 and I saw few ram bytes available.I switched to an Arduino Mega and I resolved.I also investigate the GSM library to see where memory buffer for SMS are allocated , but for me is not easy to change library.

Sounds like a serialBuffer problemWhat are you using to comunicate with the modem?(softserial , native UART,newsoftserial???)

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The native serial support happens via a piece of hardware (built into the chip) called a UART. This hardware allows the Atmega chip to receive serial communication even while working on other tasks, as long as there room in the 64 byte serial buffer.

The problem could be you are not reading the incoming data fast anought and then the serialBuffer overflowPost all the code